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There seem to be certain clues throughout the books that dragonriding ability is linked to an inherited trait. All the dragonriders are Targaryens or are linked somehow to Valyrian ancestry. So let's assume that there is a genetic component linked to dragonriding ability.

We can then look at the examples from Fire & Blood to get a sense of what this genetic component is. We are given two clear examples where a dragonrider produces offspring with a mate of non-Valyrian descent - Viserys's four children by Alicent Hightower and Rhaenyra's three children by Harwin Strong. These 7 children all grow up to be dragonriders. If dragonriding is a recessive trait, the probability of this outcome is 1 out of 128 (2 to the 7th power) or less than 1% (we have to assume that both Alicent Hightower and Harwin Strong are somehow carriers which needs an explanation - the other situation where both have the genetic ability without displaying it is even more implausible). This is the simplified case of Mendellian inheritance. In a more complex case, where multiple genes factor in, the probability of this outcome is even lower. This is a very unlikely outcome.

We also have four other instances of a dragonrider producing offspring with a non-dragonrider - Aenys had six children by Alyssa Velaryon (whose mother was a Massey), Aemon had one child with Jocelyn Baratheon (whose mother was Alyssa Velaryon), Rhaenys had two with the Sea Snake and Viserys had one child with Aemma Arryn. All four of these examples are less clear cut but the results (all but 2 of these 10 children are dragonriders - one of the 2 non-dragonriders died in infancy and the other died at the age of 15 without any opportunity to claim a dragon) add to the overwhelming evidence that whatever genetic component that may be a necessary pre-requisite for dragonriding ability has to be a dominant trait.

Therefore, we can come to one of three conclusions. The first is that genetics and dragonriding inheritance doesn't work at all like our genetics and there is some magical component that has yet to be revealed. The other two conclusions are either that this genetic trait is either much more widespread than assumed or it is a dominant trait, meaning that a dragonrider needs only to have one parent with the ability to be a dragonrider in order to express this genetic trait. These final two conclusions lead to some contradictions though. Quentyn Martell's failure provides one contradiction of a strong genetic component. And earlier, the numerous failures during the sowing of the seeds contradicts both the idea that this genetic trait is either dominant or widespread.

All the evidence points to some other magical means by which dragonriders form a connection with their dragon. There still remains much that is unexplained about how dragonriding works. If there is some soft genetic component that is necessary to provide a predisposition then there is something magical at work. Regardless, much of becoming a dragonrider must be more than just inheritance. There must be some factors that are learned traits of some kind.

One explanation that occurs to me for the way the inherited aspect works relates to the Targaryen affinity with fire. We see that Dany has this (she likes her baths very very hot and is able to withstand heat that others cannot), and we see with Egg as well that he had a similar affinity with heat. Quentyn Martell has Targaryen ancestry, but he also can trace his ancestry back to Nymeria of the Rhoyne. The Rhoynar were supposed to have some kind of water magic which perhaps cannot co-exist with the fire magic of the Valyrians. If this is the case, both Egg and Dany can trace their ancestry back to Nymeria as well, so after these marriages of fire and water the resulting offspring would be less likely to display this fire trait which is impossible to say anything else about considering there were no dragons around to provide proof one way or the other for this theory.

Whatever the shape of this thing is, the fact of the case must be that whatever part of dragonriding that relates to an inherited trait must be at this point fairly widespread throughout Westeros (and Essos as well), which means that there should be quite a large number candidates who could potentially ride Rhaegal and Viserion.

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Princess Daenarys Targaryen married Prince Maron in 187, and Quentyn's father was born in 247. There should be 4 or 5 generations between them, meaning that Quentyn would have has only 1/32th or 1/64th of Targaryen blood.

I assume that you need a much higher degree of Valyrian blood to ride a dragon. All the dragonseeds (except Neetles) had the typical Valyrian features, so I'd guess their Valyrian ancestor was closer than that.

But let's remember that this is the same book where Baratheons and Lannisters can only produce black haired descendants, and ruling members of many families maintain the same distinctive traits for centuries. George just doesn't care about portraying anything close to a genetically realistic world.

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22 minutes ago, The hairy bear said:

But let's remember that this is the same book where Baratheons and Lannisters can only produce black haired descendants, and ruling members of many families maintain the same distinctive traits for centuries. George just doesn't care about portraying anything close to a genetically realistic world.

Well. The inheritance of dragonriding clearly doesn't follow any kind of probabilistic model so it is not genetic in the way we understand inheritance of genes. The hair color thing is realistic enough to relate to our world. The characters didn't draw perfectly scientific conclusions from the evidence, but the evidence is close enough to our reality to make sense.

25 minutes ago, The hairy bear said:

Princess Daenarys Targaryen married Prince Maron in 187, and Quentyn's father was born in 247. There should be 4 or 5 generations between them, meaning that Quentyn would have has only 1/32th or 1/64th of Targaryen blood.

I assume that you need a much higher degree of Valyrian blood to ride a dragon. All the dragonseeds (except Neetles) had the typical Valyrian features, so I'd guess their Valyrian ancestor was closer than that.

This is not at all how inheritance works in our world. If the percentage of Valyrian blood has something to do with it in GRRM's world, well then what is the threshold? The Targaryens have been marrying non-Valyrians for many generations by the time Dany pops out. This percentage thing doesn't hold water. We've seen in Fire & Blood that dragonriders keep popping out consistently over several generations of intermarriage. If there is something inherited, the rule of inheritance is a strong one, whatever it is.

That's why I think there's something magic-related going on. The dragonriding thing is too central to the story for GRRM to not have a fully fleshed-out explanation. If there is not some sort of consistent rule for the way this thing works, I'd be very surprised.

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I've been thinking about this and this is what I've established so far:
- Targaryens believe that ability to hatch and ride dragons is within their blood. But this might be superstition.
- The best way of keeping the ability within the family is to marry each man in a family to a woman in the same family, because it is easier to trace woman parentage.
- Targaryens have cadet families that carry the dragonblood. Whenever there are excessive females in a generation of Targaryens, they will marry them to those families. If the opposite occurs (there is not enough females to pair with males) they will call for women descended from Targaryen females from those families.
- The cadet families are: Valeryon, Baratheon, possibly Celtigar. At some point Arryn served the role. There are "leaks" to other families as well, for example Hightowers - not all bloodlines are possible to trace.
- Important female figures in Targaryen and Valeryon families are in control of the eugenic project and investing heavily in it.
- Hightowers, maesters and Faith repeatedly attempt to disrupt or take control of Targaryen bloodline.
- Inheriting the ability is not mother related and probably not even gender related (you can inherit from a man as well).
- It (most probably) doesn't go with X chromosome either.
- Twins share the ability. Siblings not necessary.
- Couldn't (so far) establish the connection between ability getting watered down and dragons going extinct.
- Couldn't (so far) establish the connection between ability and monstrous miscarriages and infertility.
- People of "strong blood" descended from generations of valyrian females have powerful presence which might imply the ability

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The ability to bond with dragons is an inherited trait.  That is the whole purpose of the Valyrian custom of brother-sister marriages.  

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Valyria was an empire, and some illegitimate Valyrian bastards have shown the ability to ride dragons. Nettles is a primary example. She's a dragonseed on Dragonstone, so a half-Targ with distinctly non-Targ features. And yet she managed to ride a dragon. It seems obvious that the dragonriding ability has to be inherited in some manner considering what we see in the books. And yet, how it appears is kind of inconsistent. It's possible GRRM made a mistake. Understandable as he started writing these books a long time ago and our understanding of genetics has vastly improved since then. 

It's also very possible that there's more than one trait that need to get passed down the generations to get the dragon riding ability. That might be why some descendants inherit physical Valyrian features, but can't ride dragons, while other descendants don't physically look Valyrian, but can ride dragons. Maybe the Targs practiced incest because marrying one another increases the chance of offspring inheriting multiple traits at once that makes it possible to ride dragons. 

On 5/6/2019 at 10:09 PM, Syl of Syl said:

The first is that genetics and dragonriding inheritance doesn't work at all like our genetics and there is some magical component that has yet to be revealed.

My pet theory is that blood magic and sacrifice also plays a big role here. The Targs since Aegon I have dragons, but they don't seem to know much about magic. They don't offer any sacrifices to the fire or anything. And eventually overtime, the dragons they have dwindle in number, and physically gets weaker and smaller. And the family starts the war with itself too. It's possible the overall disappearance of magic from the world is the cause here or the maester conspiracy as some people say. Or it's possible that the Valyrians in exile have forgotten their ways and they lose dragons. 

Dany ultimately gets her dragons in a fire magic, blood sacrifice ritual. Her kin go into the fire, dragons come out, and she can ride one without getting burnt to death. GRRM has yet to reveal how a dragonrider can control a dragon as well. In ADwD, Dany realizes that riding a dragon isn't anything like riding a horse. Drogon doesn't necessarily follow her command. But there are some vague hints that it's her will that Drogon follows. 

Even if blood sacrifice is necessary to make or hatch dragons, how it gives the dragon affinity is still really confusing. I mean, Dany makes the sacrifice, but how does it pass down to her children (if she could have any)? I suppose there are magical blood ties that aren't really related to genetics, but the type of blood bonds that appear in magical fantasy worlds. You know like curses that pass down the generations. But in this case, dragons. 

Also, Dany in ADwD says that Drogon is fire made flesh, but so is she. The blood of old Valyria is human as far as we know. But they do have distinctive features, like pale skin, purple eyes, and silver hair no other people on earth have. These same features, especially the paleness, is associated with certain magic things, the White Walkers, the pale gods, and pale things that Septon Barth pulls out of Princess Aerea. So the genetics for them work differently because the Valyrians themselves aren't exactly human?

 

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